Solution: Developing an automated translation system utilizing machine translation - DocstringTranslation.jl 😎
A package for translating Julia docstrings into any preferred language
@doc exp (Original)
julia> @doc exp
exp(x)
Compute the natural base exponential of x, in other words ℯ^x.
See also exp2, exp10, and cis.
Examples
≡≡≡≡≡≡≡≡
julia> exp(1.0)
2.718281828459045
julia> exp(im * pi) ≈ cis(pi)
true
exp(A::AbstractMatrix)
Compute the matrix exponential of A, defined as:
e^A = \sum_{n=0}^{\infty} \frac{A^n}{n!}.
For symmetric or Hermitian matrices A, an eigendecomposition (eigen) is used; otherwise, the scaling and squaring algorithm
(see [^H05]) is employed.
│ [^H05]
│
│ Nicholas J. Higham, "The squaring and scaling method for the matrix exponential revisited", SIAM Journal
│ on Matrix Analysis and Applications, 26(4), 2005, 1179-1193. doi:10.1137/090768539
│ (https://doi.org/10.1137/090768539)
Examples
≡≡≡≡≡≡≡≡
julia> A = Matrix(1.0I, 2, 2)
2×2 Matrix{Float64}:
1.0 0.0
0.0 1.0
julia> exp(A)
2×2 Matrix{Float64}:
2.71828 0.0
0.0 2.71828@doc exp (Translated into Japanese)
julia> ENV["OPENAI_API_KEY"] = "sk-<blah>"
julia> using DocstringTranslation
julia> @switchlang! :ja
julia> @doc exp
exp(x)
Compute the natural base exponential of x, in other words ℯ^x.
Also see exp2, exp10, and cis.
Examples
≡≡
julia> exp(1.0)
2.718281828459045
julia> exp(im * pi) ≈ cis(pi)
true
exp(A::AbstractMatrix)
Compute the matrix exponential of matrix A, defined as:
e^A = \sum_{n=0}^{\infty} \frac{A^n}{n!}.
For symmetric or Hermitian matrices A, an eigendecomposition (eigen) is used; otherwise, the scaling and squaring algorithm
(see [^H05]) is employed.
│ [^H05]
│
│ Nicholas J. Higham, "The squaring and scaling method for the matrix exponential revisited", SIAM Journal
│ on Matrix Analysis and Applications, 26(4), 2005, 1179-1193. doi:10.1137/090768539
│ (https://doi.org/10.1137/090768539)
Examples
≡≡
julia> A = Matrix(1.0I, 2, 2)
2×2 Matrix{Float64}:
1.0 0.0
0.0 1.0
julia> exp(A)
2×2 Matrix{Float64}:
2.71828 0.0
0.0 2.71828